The book is a historical investigation of the problem of infinity in Greek ontology and physics more specifically, the problem of the infinite size of the world and of its eternal existence, the problem of the infinity of worlds, of infinite divisibility of matter, of infinity of attributes or attribute modes (e.g., infinity of atom shapes), and the problem of infinity of nonphysical entities such as mathematical constructs. The view espoused here is that infinity was of paramount importance for Greek philosophers even if it was not explicitly discussed by them. It served as an unspoken assumption without which Greek philosophy could hardly be possible.